作为局部体场的威尔逊塔
Wilson Towers as Local Bulk Fields
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中文总结 AI 辅助
研究2+1维引力中威尔逊线轴与局部自由场关系，用对称函数方法将热AdS₃中威尔逊线轴重铸为单缠绕威尔逊圈和，通过多迹原初场后代与边界引力子重现维拉索罗特征，获BTZ柄体单圈行列式微观描述，强化光滑视界与量子态系综关系观点。
中文摘要 AI 辅助
在2 + 1维引力中的多缠绕威尔逊圈（“威尔逊线轴”）可以重现体中局部自由场的单圈配分函数。体自由场有二次量子化的福克空间，AdS/CFT对应表明相关的多粒子扇区与CFT中的多迹原初场对偶。本文用标准对称函数方法表明热AdS₃中的威尔逊线轴可重铸为单缠绕威尔逊圈的和，每个多迹原初场对应一个。还表明多迹原初场的SL(2)后代与AdS₃背景的边界引力子能正确重现每个模的完整维拉索罗特征。这能得到光滑BTZ柄体上单圈行列式的“微观”描述。空间缠绕在有可收缩热循环的环面上的探测威尔逊线可换成插入密集重玻色子圈族上的维林德线，且两个循环角色互换。模S核的真空行充当重原初场的（近似）密度。这加强了arXiv:2601.18775中的观点，即光滑视界是量子态系综的替身，每个量子态由重威尔逊线产生，在半经典极限下表现为奇异视界。
英文摘要
Multi-winding Wilson loops (``Wilson spools'') in 2+1-dimensional gravity can reproduce one-loop partition functions of local free fields in the bulk. Bulk free fields have a second-quantized Fock space, and the AdS/CFT correspondence suggests that the associated multi-particle sectors are dual to multi-trace primaries in the CFT. In this note, we use standard symmetric-function methods to show that the Wilson spool in thermal AdS$_3$ can be recast as a sum over $single$-winding Wilson loops --- one for each multi-trace primary. In a companion paper to appear, we will view Wilson networks and TQFTs as the natural language of non-perturbative bulk quantum gravity. The present note illustrates how this can apply to $local$ bulk fields, and not just defects: a bulk (generalized free) field is to be viewed as a full tower of multi-trace Wilson lines. We further show that the $SL(2)$ descendants of each multi-trace primary, together with the boundary gravitons of the AdS$_3$ background, correctly reproduce the full Virasoro character of each module. In this language, the role of a light insertion on a heavy primary is played by a topological Verlinde line. This allows us to obtain a ``microscopic" description of one-loop determinants on the smooth BTZ handlebody. A spatially wound probe Wilson line on a torus with a contractible $thermal$ cycle can be traded for a Verlinde line inserted on a dense family of heavy Polyakov loops --- with the roles of the two cycles exchanged, so that the $spatial$ cycle is now contractible. The vacuum row of the modular $S$-kernel acts as the (approximate) density of the heavy primaries. This reinforces the case made in arXiv:2601.18775 that a smooth horizon is a stand-in for an ensemble of quantum states, each produced by a heavy Wilson line that appears as a singular horizon in the semi-classical limit.
